In this article of HDR insight series, you’ll learn more about transfer functions, and two specific transfer functions for High Dynamic Range, PQ & HLG.

1. HDR Insights Article 2 : PQ and HLG
transfer functions for HDR
In the previous article HDR introduction, we discussed the benefits HDR
(High Dynamic Range) brings about in terms of quality of the video. This article
talks about how that is achieved.
To display the digital images on the screen, display devices need to convert
the pixel values to corresponding light values. This process is usually non-
linear and is called EOTF (Electro-Optical Transfer Function). Different types
of “Transfer Functions” are supported in different display devices.
Regular HDTV display devices (SDR – Standard Dynamic Range – monitors)
normally use BT.709 Gamma transfer function to convert the video signal into
light. These monitors are primarily designed to display images with brightness
range of up to 100 Nits (cd/m2).

2. High Dynamic Range – Transfer
Functions (PQ & HLG)
HDR defines two additional transfer functions to handle this issue – Perceptual
Quantizer (PQ) and Hybrid Log-Gamma (HLG). HDR PQ is an absolute,
display-referred signal while HDR HLG is a relative, scene-referred signal.
This means that HLG enabled display devices automatically adapts the light
levels based on the content and their own display capabilities while PQ
enabled display devices need to implement tone mapping to adapt the light
levels. Display devices use content metadata to display PQ coded images.
This can come once for the entire video stream (static) or for each individual
shot (dynamic)
It is expected that under ideal conditions, dynamic PQ based transformation
will achieve the best quality results at the cost of compatibility with existing
display systems. Please see examples below:
HDR – Signal to light mapping
The graph below describes the mapping of light levels for various transfer
functions. Vertical axis shows the signal values on a scale of 0-1 with 0 being
black and 1 being white. This is done to make the signal range, bit depth
agnostic. Horizontal axis shows the light level in Nits of display device.

3. Human beings are more sensitive to changes in darker region compared to
changes in brighter regions. This property is also exploited in HDR systems
providing more granularity in darker regions compared to brighter regions. The
graph above depicts that light level range in darker region is represented by a
larger signal value range compared to the brighter regions – meaning more
granular representation in darker regions. While this is more evenly distributed
for the BT.709 based displays, it become less granular for HDR displays in the
brighter regions. In case of HLG, more than half of signal values are
represented for light level between 0-60 Nits and the remaining signal values
are represented in 60-1000 Nits range. Similarly, in case of PQ ST2084 based
displays, approx. half of the signal values are represented for light level
between 0-40 Nits and the remaining half of signal values are represented in
60-1000 Nits range.
According to the graph, HDR HLG is similar to BT.709 in lower brightness
regions therefore offering a better compatibility with the existing SDR display
devices. However, HDR PQ is quite different from BT.709. If we try to display
the PQ HDR image on a SDR display, darker regions represented by PQ will
invariably become brighter thereby reducing the contrast levels of the image,
the result being a washed out image (see below)

4. HLG based image looks much better on a SDR monitor:
While PQ based transforms offers promise to display best quality results on
HDR enabled monitors, in comparison to HLG, it requires proper tone mapping
by display devices.
This topic will be discussed in our next blog article – Tone mapping.
Definitions
cd/m2 – The candela (cd) is the base unit of luminous intensity in the
International System of Units (SI); that is, luminous power per unit solid angle
emitted by a point light source in a particular direction. A common wax candle
emits light with a luminous intensity of roughly one candela.
Nits – A non-SI unit used to describe the luminance. 1 Nit = 1 cd/m2.

5. HDR – High Dynamic range. It is a technology that improves the brightness &
contrast range in an image (up to 10,000 cd/m2)
SDR – Standard Dynamic range. It refers to the brightness/contrast range that
is usually available in regular, non-HDR televisions usually with range of up to
100 cd/m2. This term came into existence after HDR was introduced
WCG – Wide Color Gamut. Color gamut that offer a wider range of colors than
BT.709. DCI-P3 and BT.2020 are examples of WCG offering more realistic
representation of images on display devices.
EOTF – electro-optical transfer function. A mathematical transfer function that
describes how digital values will be converted to light on a display device.
OETF – optical-electro transfer function. A mathematical transfer function that
describes how the light values will be converted to digital values typically
within cameras.
OOTF – opto-optical transfer function. This transfer function compensates for
the difference in tonal perception between the environment of the camera and
that of the display.
PQ – PQ (or Perceptual Quantizer) is a transfer function devised to represent
the wide brightness range (up to 10,000 Nits) in HDR devices.
HLG – HLG (or Hybrid Log Gamma) is a transfer function devised to represent
the wide brightness range in HDR devices. HLG is quite compatible with
existing SDR devices in the SDR range.
Originally Published at:- https://www.veneratech.com/hdr-transfer-functions-hlg-pq/